The Ground State Properties Of Rotating Bose-Einstein Condensates In An Annular Trap

The ground state density distribution of the single Bose-Einstein condensates (BECs) or two component BECs can experience a transition from the vortex lattice to giant vortex ether when the angular frequency increases and the width and the center height of the trap potential are fixed, or when the width and the center height of the trap increase and the angular frequency is fixed. More importantly, with the increasing of the rotating frequency or the width and the center height of the annular trap, more interesting ground state density profiles will be present. In this paper, we start with the Gross-Pitaevskii (GP) equation, and obtain the ground states of BECs by using the Thomas-Fermi approximation (TFA) method and the numerical method respectively and discuss their corresponding properties. The main contents are given as follows:In the first part, we introduce the concept of Bose-Einstein condensate (BEC) and its implementation in experiment. Then, we make a brief description about the forming principle of vortex and spin texture. Lastly, the numerical method for solving the GP equation is presented in detail.In the second part, we introduce the GP equation model at first, which can be used to research the ground states and the dynamic behavior of single BECs. Then, we use the TFA method to obtain the critical angular frequency and the critical width and center height of the annular trap in which the BECs changes from a disc shape to an annular shape. Lastly, we discuss the ground state properties of the annular BECs with the increase of the angular frequency, or with the increase of the width and the center height of the annular trap.In the third part, the coupling GP equation model is firstly introduced, which can be used to research the ground states and the dynamic behavior of two component BECs. Then, we use the TFA method to investigate the critical angular frequencies and critical widths and center heights of the annular trap in which two component miscible BECs can change from disc shape to annulus shape respectively. Lastly, we use the imaginary-time propagation method to investigate the changes in the ground state density profiles and phases of the two-component immiscible BECs with the increase of the angular frequency or with the increase of the width and the center height.In the last part, we summarize the main content of this paper and present the task to be completed.